The original question:

What do you think is the probability that the IQ you gave earlier in the survey is greater than the IQ of over 50% of survey respondents?

Well, the predictions spread the usual range and look OK to me:

R> lwci <- as.numeric(as.character(lw$CalibrationIQ))
R> lwci <- lwci[!is.na(lwci)]
R> # convert tiny decimals to percentages & put a ceiling of 100 (thanks to Mr. 1700...)
R> lwci <- sapply(lwci, function(x) if (x<=1.00) { x*100 } else { if(x>100) { 100 } else { x }})
R> summary(lwci)
Min. 1st Qu. Median Mean 3rd Qu. Max. 0.0 20.0 50.0 44.8 70.0 100.0